Martin noted that he was not there to negotiate new incentives for RBS, but to update the company about his perception of Stamford's future and RBS's role in it.

"They would not precisely say what their exact plans are, but I think we remain sensitive to their needs," Martin said.

He added he didn't feel the job cuts would affect the city too significantly, and that there are other areas of RBS's business based in the city that are much larger.

"I don't think it's going to have a major ripple effect on Stamford or its downtown," Martin said.

RBS has around 2,000 employees in Stamford and is the third-largest employer in the city, according to Stamford's 2013 annual report. The bank first moved to Stamford in 2009, in the midst of the financial crisis. RBS now inhabits a 12-story, 540,000-square-foot building on Washington Boulevard.